I seen a question on a practice paper a while back which confused me a 'lil. Here it is:
Source: Edexcel GCE Core Mathematics C1 AS - Monday 10th Januaryy 2005
The gradient of the curve C is given by
The point P(1,4) lies on C. (For reference, but was used for questions A and B)
c) Using dy/dx, show that there is no point on C at which the tangent is parallel to the line
I don't know where to start on this question, so any help would be great :x, especially since I have a C1 exam in ~ 2 hours. D:
So far, all I know is that the gradient of is obviously -2 and the increment (+1) doesn't matter (hence, parallel).
So those are the 2 gradients of the equasion, and I have no idea on how to show that there's no point on C where they're parallel.
parallel means they have the same slope. so you need to show that dy/dx = -2 is never true.
Originally Posted by Bladescope
this should be somewhat obvious. dy/dx is a square, and is thus greater than or equal to zero for all x, while -2 < 0. they cannot be equal
thus, dy/dx never matches the slope of the line in question and so there is no tangent line that is parallel to the said line